Identidades y derivadas trigonométricas

IDENTIDADES TRIGONOMETRICAS
22
Sen A + Cos A = 1
22
Sec A = 1 Tan A
22
Sec A = 1 Cot A
Formulario de Derivadas
• Dx (c) = 0
2
• Dx ( x )
• Dx [ c * f ( x ) ] = c * Dx f ( x )
n n−1
• Dx ( cx ) = cn X (N entero positivo)
• Dx [ f ( x ) + g ( x ) ] = Dx f ( x ) + Dx g ( x )
• Dx f1 ( x ) + f2 ( x ) + ... + fn ( x ) ] = Dx f1 ( x ) + Dx + 2 ( x ) + ... + Dx fn ( x )
• Dx [ f ( x ) + g ( x ) ] = f ( x ) * Dx g ( x ) + g ( x ) Dx f ( x )
8. Dx f ( x ) = g ( x ) * Dx f ( x ) − f ( x ) Dx g ( x )
g(x)2
g(x)
r r −1
9. Dx ( x ) rx r es un numero real
r r −1
1
Dx ( cx ) crx
Derivadas de las funciones trigonométricas
10. Dx ( Sen x ) = Cos x
11. Dx ( Cos x ) = −Sen x
2
12. Dx ( Tan x ) = Sec x
2
13. Dx ( Cot x ) = Csc x
14. Dx ( Sec x ) = Sec x Tan x
15. Dx ( Csc x ) = Csc x Cot x
Derivadas de funciones logarítmicas y exponenciales
16. Dx ( Ln x ) = 1
x
17. Dx ( e ) = e
18. Dx ( a ) = a ln a
19. Dx ( log a x ) = log a e
Dx ( log a x ) = 1
x * ln a
2
20. Dx ( Sen X) = 1
1− x
21. Dx ( Cos X) = 1
1+x
22. Dx ( Tan X ) = 1
1+x
23. Dx ( Cot X ) = 1
1+x
24. Dx ( Sec X ) = 1
X X −1
25. Dx ( Csc X) = 1
X X −1
Derivadas de las funciones hiperbólicas
26. Sen h X = e − e ; Dx ( Sen h X ) = Cos h ; Dx (Sen h U ) = Cos U * Dx
2
27. Cos h X = e + e ; Dx ( Cos h ) = Sen h X ; Dx ( Cos h U) =
2
28. Tanh X = Sen h x = e − e ; Dx ( Tan h X ) = Sec h X ; Dx ( Tan h U ) =
Cos h X e + e
29. Cot h X = Cos h X = e + e ; Dx ( Cot h X ) = − Csc X ; Dx ( Cot h U ) =
Sen h X e − e
30. Sec h X 1 = 2 ; Dx ( Sec h X ) = − Sec h X Tan h X ; Dx ( Sec h U ) =
Cos h X e + e
31. Csc h X 1 = 2 ; Dx ( Csc h X ) = − Csc h X Cot h X ; Dx ( Csc h U ) =
3
Sen h X e + e
4